BESSELK in Collabora Office: Model Modified Second-Kind Bessel Decay

=BESSELK(X; N)

X is the strictly positive evaluation point. N is the order, including zero under the help’s explicit N ≥ 0 condition. Both are required. For a positive fractional order input, Collabora’s example shows that the fractional part is discarded: 4.333 uses order four.

BESSELK computes the modified second-kind function Kₙ(x). Its meaning is not interchangeable with the ordinary second-kind function Yₙ(x), or the modified first-kind function Iₙ(x). A similar-looking function name does not establish numerical equivalence.

The explicit vendor error example is =BESSELK(0;3), which returns Err:502, described as an invalid argument because X is zero. A zero input is therefore not a way to obtain the limiting value at the origin.

Enter A2:B7 as shown, then put =BESSELK(A2;B2) in C2 and fill down. Expected figures below are independent mathematical values rounded to nine decimal places.

Keep X positive when extending the table. If your physical model contains a scaled input, such as radius divided by a characteristic length, calculate and inspect that ratio separately. A valid positive radius does not rescue an invalid zero denominator elsewhere in the model.

Use scientific notation if small values disappear as displayed zeros. An ordinary number format can conceal a small nonzero result; formatting is not evidence of mathematical zero.

Collabora documents the same value, 0.144803466373734, for =BESSELK(3.45;4) and =BESSELK(3.45;4.333). An independent high-precision K₄(3.45) evaluation is approximately 0.144803465889659.

Those figures agree when rounded to six decimal places, 0.144803, but differ in later digits. This guide preserves that distinction rather than presenting the published example as a fresh native accuracy measurement. The source’s fractional-order behavior is explicit; the origin of the small numeric discrepancy is not established here.

If later digits matter to your application, validate the actual Collabora version and numerical tolerance against an appropriate reference before relying on those digits.

Enter 1, 2, 3 in E2:E4. In F2 use =BESSELK(E2;0) and fill down. In G2 use =F2/$F$2 and fill down. G2 should be one under the independent model; G4 is approximately 0.082511848.

Thus the K₀ value at X=3 is approximately 8.2511848% of its value at X=1. The relative reduction is approximately 91.7488152%, calculated by =1-G4 and displayed as a percentage.

This is a ratio of modeled function values. It is not a percentage loss in every physical system that contains a Bessel function: scaling constants, boundary conditions, and other model terms may change the interpretation.

The mathematical identity K₂(x)=K₀(x)+2K₁(x)/x yields this check at X=2:

=BESSELK(2;2)-BESSELK(2;0)-BESSELK(2;1)

Its independent residual is zero: 0.253759754566056 − 0.113893872749533 − 0.139865881816522. A small floating-point residual should be judged with a justified tolerance. ABS is useful for its magnitude; ROUND is a display choice, not an accuracy guarantee.

For Err:502, start by checking the documented strict-positive X requirement. Negative X and negative orders are outside the stated contract; this guide does not extend the documented zero-input error code to every invalid case.

The function-specific help does not provide a complete coercion matrix, native overflow/underflow thresholds, or certified precision range. Keep the raw inputs, verify the family and order, and test moderate controls before interpreting extreme results.

The exact function is documented in Collabora Office 26.04 desktop help, retrieved and reviewed on October 17, 2026. This establishes a documentation scope, not the first release that introduced the function or the last version in which it works; those versions and any retirement date remain unestablished. Collabora Online and mobile support are not inferred from desktop help, nor is behavior in another spreadsheet product.

The examples are documentation-based expectations with independent calculations. They have not been executed in Collabora Office. No application screenshot or native error/coercion certification is implied. Formulas use English function names and semicolon argument separators.

• Collabora Office 26.04: BESSELK (checked October 17, 2026).
• Editorial testing standards.